[Math] Can you provide me historical examples of pure mathematics becoming “useful”

Question

I am trying to think/know about something, but I don't know if my base premise is plausible. Here we go.

Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because it has no practical utility, but I guess that according to the history of mathematics, the math that is useful today was once pure mathematics (I'm not so sure but I guess that when the calculus was invented, it hadn't a practical application).

Also, I guess that the development of pure mathematics is important because it allows us to think about non-intuitive objects before encountering some phenomena that is similar to these mathematical non-intuitive objects, with this in mind can you provide me historical examples of pure mathematics becoming "useful"?

Answer 1

Here are few such examples

• Public-key cryptosystems based on elliptic curves, factorization, trapdoor functions, lattices and hyperelliptic curves.
• Use of algebraic topology in distributed computing and sensor networks. Topology has uses in various other branches engineering as well.
• Use of differential geometry for computer graphics, computer vision algorithms, robotics and general relativity.
• Error-correcting codes based on algebraic geometry. Algebraic geometry has also applications in robotics.
• Lattice theory is used in program analysis and verfication.
• Group theory is used in chemistry as well as physics
• Tropical geometry, a branch of algebraic geometry, has applications in mathematical biology.
• Digital electronics is impossible without Boolean algebra.
• Topos theory has been applied to music theory